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July 2004 - present
Publications
Publications (53)
This chapter focuses on teaching the use of programming technology for pure or applied mathematics investigation projects to university mathematics students and future mathematics teachers. We investigate how the theoretical frame of instrumental orchestration contributes to our understanding of this teaching. Our case study is situated within the...
We are interested in understanding how university students learn to use programming as a tool for “authentic” mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of development of sc...
The creation of new and innovative working spaces in post-secondary mathematics education that involve both powerful instructional technologies and more traditional paper/pencil techniques require changes in both curricular scope and related assessment practices. In this chapter, researchers highlight the recent reporting of findings from their cas...
In this paper, we recount our research on undergraduate mathematics students learning to use programming for mathematics investigation projects. More precisely, we focus on how a particular theoretical perspective (the Instrumental Approach) helps us better understand this student activity. Pulling data from students' and instructors' experiences i...
In this naturalistic study, we examine students' learning as they engage in programming for mathematics investigations through a project-based approach. We focus on undergraduate mathematics students' (N=41) engagement in a sequence of 14 programming-based math investigation projects, with data primarily collected through online questionnaires. Res...
In this paper, we present an empirical study examining challenges undergraduate mathematics students (N=73) encounter when engaging in programming-based mathematics inquiry projects, and how they handle these challenges. Results suggest that a majority of students find the programming or the programming of mathematics the most challenging aspect of...
In this article, we seek to understand how university students learn to use programming as an instrument for ‘authentic’ mathematical investigations. We use the instrumental approach as a framework, focusing on how the transformation of the programming language into an instrument requires that the user develops or mobilizes multiple schemes at diff...
E-Brock Bugs is a serious educational game (SEG) about probability which was created based on Devlin's design principles for games whose players adopt identities of mathematically able persons. This kind of games in which “players think and act like real world professionals” has been called epistemic. This chapter presents an empirical study of 16-...
The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument (i.e. an artefact and schemes developed by the student). In this paper, we articulate the instrumental approach for co...
In this paper, we report on a case study that focused on innovative uses of CAS technology in university mathematics teaching and assessment. The study involved a site visit to the University of Alberta campus (June 2015) during which: interviews were conducted with five mathematics faculty members and seven mathematics students; math lectures were...
E-Brock Bugs is a serious educational game (SEG) about probability which was created based on Devlin's design principles for games whose players adopt identities of mathematically able persons. This kind of games in which "players think and act like real world professionals" has been called epistemic. This article presents an empirical study of 16-...
Since 2001, undergraduate mathematics majors and future mathematics teachers at Brock University (Canada) learn through a sequence of three courses to use programming to conduct mathematical inquiries or investigate real-world applications. In this paper, we provide a rich description of the assessment process of mathematics implemented in these co...
![Figure 1: Brock Bugs board game -the cardstock version [7].](profile/Chantal-Buteau-2/publication/313262871/figure/fig1/AS:457787072356352@1486156351647/Brock-Bugs-board-game-the-cardstock-version-7_Q320.jpg)
/ Synopsis
In the Fall of 2013 our team of three different generations of mathematicians launched the free, online E-Brock Bugs© mathematics computer game [5] which we developed from an original probabilistic board game, Brock Bugs, and its digital learning object version. We constructed E-Brock Bugs using Devlin’s [9] mathematics computer game des...
In 2011, the European Mathematical Society stated that a third pillar of scientific inquiry of complex systems has emerged in the form of a combination of modelling, simulation, optimization and visualization. This paper presents a naturalistic case study of an undergraduate student enrolled in a sequence of three programming, project-based mathema...
In a sequence of core mathematics courses instituted in 2001 at Brock University, students learn to design, program and use interactive computer environments, in order to investigate a self-stated mathematical conjecture, a concept, a theorem or a real-world situation. In this article, we provide documentation for the complete implementation proces...
/ Synopsis
Devlin in [7] argues that video games are an ideal medium for the teaching and learning of mathematics, though he points out that very few ’good’ mathematics video games exist. Building on a probabilistic board game developed in the 1980s, we created a mathematics computer game, E-Brock Bugs. The design of the game carefully follows Devl...
We discuss the dual teaching roles of university mathematics tutors, as teachers and policy makers, in relation to the classroom implementation of technology while guided by departmental policies. The main contribution of this chapter is the exemplification of these roles in an undergraduate mathematics programme, called Mathematics Integrated with...
In this article we present an instrumental approach in mathematics education, which focuses on the interactions between students, teachers, and artefacts. This approach analyses mediations attached to the use of a given artefact and instruments developed by the subjects from this artefact along instrumental geneses. We draw on three Research Cases...
This article is centred in university mathematics education. It reports the results of an extension to a research literature
study identifying the competencies that mathematics majors acquire as they learn mathematics within the context of designing,
programming and using Exploratory Objects, a requirement in a core mathematics programme called Mat...
As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory...
This paper reports on the findings of an international case study in which researchers examined two mathematics departments (Canada/UK) in which the sustained use of technology was strategically established in a mathematics degree program. This case study forms part of a larger research initiative which involved an extensive literature review (Mars...
In this article, we outline the findings of a Canadian survey study (N = 302) that focused on the extent of computer algebra systems (CAS)-based technology use in postsecondary mathematics instruction. Results suggest that a considerable number of Canadian mathematicians use CAS in research and teaching. CAS use in research was found to be the stro...
Through an analysis of the Ontario secondary school mathematics curriculum and the core mathematics program at Brock University, Windsor, Ontario, Canada, the authors provide a detailed description of what constitutes a student's intelligent partnership with technology when learning or doing mathematics. While the Ontario curriculum provides many o...
With a focus on “the use of technology in the classroom practice” and on “design and use of digital teaching materials,” this paper will report on the findings of Jarvis, Buteau, and Lavicza (2012) from their SSHRC International Opportunities Fund Project Grant research study entitled, “Computer Algebra Systems (CAS) in University Instruction: An I...
This paper revisits a mathematical model of motivic analysis, together with its computational realization, from an interdisciplinary perspective, relating it to concepts and methods in the field of computational music analysis. Issues such as segmentation, motivic formation, knowledge representation, similarity and categorization, and interpretatio...
We present a comparative study of a literature review of 326 selected contributions (Buteau, Marshall, Jarvis & Lavicza, 2010) to an international (US, UK, Hungary) survey of mathematicians (Lavicza, 2008) regarding the use of Computer Algebra Systems (CAS) in post-secondary mathematics education. The comparison results are organized with respect t...
This paper discusses a mathematical model together with its computational realization, for the motivic analysis of a piece
of music. Relations between the mathematical model (motivic topologies), computational counter-part (OM-Melos), and music
analysis are presented in the light of general concepts of computational music analysis, stressing the im...
This special issue of the Journal of Mathematics and Music addresses the topic of computational music analysis. It arose from a series of two international workshops on the topic, one in Berlin and one in Paris, both of which created interesting discussions and debates. In the call for papers, this special issue welcomed previously unpublished cont...
Using different levels of analysis, we identify some factors influencing the integration of digital technology in mathematics
and we try to explain the contradiction between the strong political will for this integration and the weak implementation
in mathematics classrooms. When one wants to change something, resistances often arise; we have ident...
We present results of a literature review pilot study (326 papers) regarding the use of Computer Algebra Systems (CAS) in tertiary mathematics education. Several themes that have emerged from the review are discussed: diverse uses of CAS, benefits to student learning, issues of integration and mathematics learning, common and innovative usage of CA...
The nature and extent of the implementation of digital technology in mathematics curricula along with issues of access and
equity were the issues considered by one working group of this ICMI study. A summary of the discussion conducted by the working
group and the findings reported in the following chapters on this theme are presented. It is clear...
This article describes a conceptual framework developed to illuminate how prospective teachers’ learning experiences are shaped by didactic-sensitive activities in departments of mathematics. We draw from the experiences of prospective teachers in the Department of Mathematics at our institution in designing, implementing (i.e. computer programming...
We outline the systemic integration and use of evolving technologies by two mathematics departments, the one in a Faculty of Engineering (in Hungary), the other in a Faculty of Mathematics and Science (in Canada). Clearly these two departments play very different roles in their institutions. In one case, the students are at the university to study...
Based on the concepts of motive contour, gestalt and motive similarity, our model of motivic structure yields topological
motivic spaces of a composition in which open neighborhoods correspond to groupings of similar motives. In Buteau 2006 we
presented a model extension of an earlier approach in order to integrate the concept of melodic clustering...
We compare four computational approaches of melodic analysis according to diverse approach aspects: input type (monophonic
or polyphonic), pattern identification type (strict or similar), analysis segmentation, aim of approach, motivic pattern representation,
and type of result representations. The considered four computational approaches are the f...
We discuss preliminary results of a literature review pilot study regarding the use of CAS in higher education. Several issues surrounding technology integration emerged from our review and are described in detail in this paper. The brief report on the type of analysis and the integration scope in curriculum suggest that the multi-dimensional theor...
This paper proposes a formalization of the neutral niveau of Rudolph Réti's approach to motivic analysis within our mathematical model based on topological spaces of motives. Réti developed a substantial approach favouring melodic relationships below the musical surface. However, his approach has been much criticized for reasons such as an evident...
This paper proposes a novel stand-alone model implementation, called OM-Melos, for the explicit construction of motivic spaces and visualization using the software OpenMusic and Maple. OM-Melos completely implements our topological model of motivic structure and analysis, including the melodic clustering model extension, unveiling all topological d...
Focus Theme 4 and issues raised in Approaches to Themes 3, 4, and indirectly 2. Abstract This submission focuses on the design of learning environments and curricula and describes a twenty five year evolution of integrating digital technology 3 in the teaching and learning of mathematics at Brock University. It provides information on actual uses o...
This paper aims at extending a topological model of motivic analysis and structure in order to insert the concept of clus-tering. Our immanent approach includes the contour simi-larity for motives of different cardinalities making possible to formalize the concept of germinal motif. Based on mo-tif, contour, gestalt, and motif similarity concepts,...
This paper presents a topological model of motivic structure and analysis of music, and its extension to comparisons of motivic analyzes. Topological T 0 -spaces of motives (called motivic spaces), their quantification for the formalization of mo-tives' "germinal function", and their graphs as motivic evolution trees (MET) form the main steps of ou...
This paper aims at presenting a topological model of motivic structure and analysis, and its application, via the implementation, to Schumann's Of Foreign Lands and People in Scenes from Childhood. Our immanent approach importantly includes the concept of contour similarity for different motif lengths making then possible to formalize the germinal...
This paper is devoted to a qualitative and quantitative study of topological spaces, the gestalt composition spaces, built on premotif collections of musical scores, and to the modelling of the motivic analysis of music. Through shape types, gestalts, and premotives distance we obtain a motivic hierarchy of a score. By reason of the non-Hausdorff a...
This paper is devoted to a qualitative and quantitative study of topological spaces built on premotif collections of musical scores. These motivic topologies are related to similarity concepts in the American music set theory. Through shapes, imitations and gestalts, and similarity relations between any two shapes, we obtain a motivic hierarchy of...
Résumé En 1999 le département de mathématiques de l'université Brock a adopté un nouveau programme de mathématiques, intitulé MICA (Mathematics Integrating Computers and Applications), dans lequel les étudiants font un usage intensif de la technologie dans tous leurs cours de mathématiques. Parmi une des nombreuses applications de l'informatique et...
In 2001 a core undergraduate program, called Mathematics Integrated with Computers and Applications (MICA) was introduced in the Department of Mathematics at Brock University, Canada. In this program that integrates evolving technologies, students complete major projects that require the design and implementation of 'Exploratory and Learning Object...
In the framework of the Distributed RUBATO platform, we propose an improved version MeloTopRUBETTE of RUBATO’s successful module MeloRUBETTE for motivic analysis. It fits with computational steering interaction and implements topological and sheaf-theoretical aspects of motive theory, such as motivic evolution trees (MET) and stalk dimensions for w...
Diss. phil. II Zürich (Austausch beschränkt). Literaturverz. Universität
Projects
Projects (3)
In 2007-12, Drs. Jarvis, Buteau, and Lavicza researched the use of CAS-based instructional technologies in undergraduate math teaching. Our SSHRC-funded projects included an extensive literature review, a national survey of Canadian mathematics professors, an international Canada/UK case study regarding math departments that have made systemic shifts in this area, two national workshops for promoting discussions, and a detailed website (http://casresearch.nipissingu.ca/). We were, and remain, particularly interested in how a move towards rich technology integration affects curriculum, learning, and assessment decisions at the post-secondary level.
